Question

Duvida sobre integrais
Por que o um ali vira um dois?

Answer 1

Resposta:

Explicação passo-a-passo:

Duvida sobre integrais

Por que o um ali vira um dois?

Answer 2

$\boxed{I=\int\limits_{x_1}^{x_2}{f(x)\mathrm{d}x}}$

$\boxed{I=\int\limits_{1}^{+\infty}{f(x)\mathrm{d}x}}$

$\boxed{I=\lim\limits_{b\to\+\infty}\int\limits_{1}^{b}{\dfrac{x}{x^2+1}\mathrm{d}x}}$

$\boxed{u=x^2+1}\ \to\ \dfrac{\mathrm{d}u}{\mathrm{d}x}=2x\ \to\ \boxed{\dfrac{1}{2}\mathrm{d}u=x\mathrm{d}x}$

$x_1=1\ \to\ u_1=x_1^2+1\ \to\ \boxed{u_1=2}$

$x_2=b\ \to\ u_2=x_2^2+1\ \to\ \boxed{u_2=b^2+1}$

$\boxed{I=\lim\limits_{b\to+\infty}\int\limits_{u_1}^{u_2}{\dfrac{1}{u}\dfrac{1}{2}\mathrm{du}}}$

$\boxed{I=\lim\limits_{b\to+\infty}\int\limits_2^{b^2+1}{\dfrac{1}{2u}\mathrm{d}u}}$